Actually Keelai just listed three anachronistic, old media wire outfits notorious for having a very leftist bias, and one rabidly partisan propaganda smear site that misleadingly calls itself "mediabiasfactcheck". In fact, contrary to his claim, I've seen numerous smaller city papers that ostensibly have a "conservative" editorial page have a completely left wing hard news A section because with smaller staffs they typically just fill it with mostly unchanged AP articles.
To answer your question we (by which I mean the modern human race) don't really have a news media. We have various propaganda outfits.
The closest I've seen to unbiased news coverage is on C-SPAN, and that's mostly because it's usually point the camera and shoot without commentary of their own, but it does seem like they've tried to be fair over the years in topic/event selection and on some of their interview shows (Brian Lamb was particularly awesome, but has unfortunately retired).
On Fox News I'll say that it's important to distinguish between their opinions shows, which usually have conservative leaning anchors, and their hard news coverage. The latter used to be so fair and balanced that you couldn't tell the personal politics of their reporters, except for Shephard Smith, the one reporter there who would routinely inject unprofessional editorial opinions into his segments, and since he's left wing was the one FNC reporter Democrats said they liked. The past couple of years have seen Rupert Murdoch's liberal sons increasingly assert control over the network in accordance with their stated desire of wanting to gradually turn it into another CNN.
While still not as bad as their competitors, FNC's hard news division has lurched into a leftist bias and typically follows the liberal media's lead on coverage (e.g. saying "undocumented immigrant" instead of "illegal alien"; Often selecting the same story coverage priorities and tone as NBC/CNN/CBS/ABC), instead of striking an independent tone as they did during the Roger Ailes era. They apparently feel they can keep their audience during this process by keeping the aforementioned conservative opinion hosts, but Fox News is doomed long term unless Rupert decides to not leave the network to his sons.